In the paper I discuss theoretical differences between left and right­libertarianism. (I will skip the specific and practical issues which differ left and right­libertarians, including among others the minorities and immigration policies or affirmative action. I assume that practical solutions suggested by the followers of both positions stem from their theoretical assumptions.) I will focus on two issues which determine the fundamental difference between left and right­libertarianism. These are property and equality. I compare standpoints of some leftlibertarians with the positions of rightlibertarians represented by Murray Rothbard, concerning property and equality. I conclude that the main and fundamental difference between leftand rightlibertarians concerns equality. Leftlibertarians are egalitarians whereas rightlibertarians are antiegalitarians. I also argue that egalitarian position is not compatible with the notion of full selfownership, which leftlibertarians advocate for.